This paper is concerned with the problem of reconstructing the qualitative values of the system states from quantized measurements of input and output sequences by means of a qualitative model. It is assumed that the state, input and output spaces are partitioned into disjoint regions. The numbers of the regions are used as qualitative values of the corresponding signals. The proposed observer uses a qualitative model of the continuous-variable discrete-time system. The model has the form of a non-deterministic automaton. A necessary and sufficient condition is given under which the observer generates a set of qualitative states that includes the qualitative state of the real system. The benefits of the observer for process supervision are shown by applying it to a tank system.